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--- b:head_first_statistics:calculating_probability [2020/09/29 15:15] – [Bayes' Theorem] hkimscil
+++ b:head_first_statistics:calculating_probability [2024/10/02 15:44] (current) – [Dependent and Independent event] hkimscil
@@ Line 30: / Line 30: @@
 A = event A
-[{{:b:head_first_statistics:pasted:20190924-173343.png|7이 일어나는 경우  }}]
+[{{:b:head_first_statistics:pasted:20190924-173343.png?850|7이 일어나는 경우  }}]
 <WRAP clear />
-[{{:b:head_first_statistics:pasted:20190924-173810.png|일반화  }}]
+[{{:b:head_first_statistics:pasted:20190924-173810.png?650|일반화  }}]
 <WRAP clear />
@@ Line 90: / Line 90: @@
 [{{:b:head_first_statistics:pasted:20190924-181909.png?400}}]
 <WRAP clear />
-[{{:b:head_first_statistics:pasted:20190926-105816.png| }}]
+[{{:b:head_first_statistics:pasted:20190926-105816.png?800| }}]
   * Intersection $ \cap $
@@ Line 137: / Line 137: @@
-[{{:b:head_first_statistics:pasted:20190924-191720.png?550}}]
+[{{:b:head_first_statistics:pasted:20190924-191720.png?800}}  ]
-[{{:b:head_first_statistics:pasted:20190924-191951.png?550}}]
+[{{:b:head_first_statistics:pasted:20190924-191951.png?800}}  ]
@@ Line 149: / Line 149: @@
 <wrap>''3/4, 1/4, 2/5, 3/5, 1/3, 2/3''</wrap>
-[{{:b:head_first_statistics:pasted:20190926-111825.png?550|Donuts Buying at Doncun}}]
+[{{:b:head_first_statistics:pasted:20190926-111825.png?650|Donuts Buying at Doncun}}  ]
-[{{:b:head_first_statistics:pasted:20190926-112041.png?550|Probability, conditional}}]
+[{{:b:head_first_statistics:pasted:20190926-112041.png?650|Probability, conditional}}  ]
 <WRAP clear />
@@ Line 160: / Line 160: @@
   * P(Coffee)
   * P(Donuts | Coffee)
+<code>
+ d (3/4) --  c [x = 3/5] [k = p(c and d)]
+         -- ~c [y = 2/5]
+~d (1/4) --  c (1/3) --> [a = p(c and ~d)]
+         -- ~c [2/3]
+x * 3/4 = p(d and c) = 9/20
+x = 9/20 * 4/3
+  = 36/60
+  = 6/10 = 3/5
+P(~d ∩ c) = a = 1/4 * 1/3 = 1/12
+P(c) = k + a
+k = 3/4 * 3/5 = 9/20
+a = 1/12
+P(c) = 54/120 + 10/120 = 64/120 = 16/30 = 8/15
+c (8/15) --  d [j]
+         -- ~d
+~c (7/15)
+j = p(d | c)
+p(d and c) = 9/20 이므로
+/15 * j = 9/20
+j = 9/20 * 15/8 = 9/4 * 3/8 = 27/32
+</code>
 </WRAP>
@@ Line 263: / Line 290: @@
 $$P(A \vert B) = \frac {P(A \cap B)}{P(B)} $$
 $$P(A \vert B) = \frac {P(A) * P(B \vert A)}{P(A) * P(B \vert A) + P(A') * P(B \vert A')} $$
 This is called "<fc #ff0000>**<fs large>Bayes' Theorem</fs>**</fc>"
@@ Line 328: / Line 356: @@
   * The probability of the ball having landed in a pocket with a number greater than 4 given that it’s red.
   * The probability of the ball landing in pockets 1, 2, 3, or 4.
 </WRAP>
+https://youtu.be/NIqeFYUhSzU?t=904
+https://youtu.be/NIqeFYUhSzU?t=1296
+https://youtu.be/NIqeFYUhSzU?t=2550
+https://wbd.ms/share/v2/aHR0cHM6Ly93aGl0ZWJvYXJkLm1pY3Jvc29mdC5jb20vYXBpL3YxLjAvd2hpdGVib2FyZHMvcmVkZWVtLzZjMjgyZjc1Y2Y0MDRhYjA4MDk5ODAyN2Y0ODZiMjlkX0JCQTcxNzYyLTEyRTAtNDJFMS1CMzI0LTVCMTMxRjQyNEUzRF83NzZhZWUxNS0yNjNmLTQ3ZWUtYWI0My1mNDM4ZDIwYzExMTI=
+Question
+  * The probability of people having the disease is 10%.
+  * The probability of test being correct is 80%.
+  * The test says that you have the disease. What is the chance you actually have the disease?
+{{:b:head_first_statistics:pasted:20230926-200603.png}}
+Question
+  * 공무를 수행하기 위해서 불법약물을 복용하는지 테스트를 한다고 한다.
+  * 사람들이 실제 약물을 수행하는 확률은 4% 라고 (0.04) 한다.
+  * 사람들이 약물을 복용하지 않는데 복용한다고 하는 테스트 결과의 (false positive) 확률은 5% 라고 한다.
+  * 약물을 복용하는데 복용하지 않는다고 하는 테스트 결과의 (false negative) 확률은 10% 라고 한다.
+  * 테스트 결과가 양성으로 나올 확률은 얼마인가?
+  * 약물을 복용한다는 테스트 결과가 나왔는데, 실제로는 약물을 복용하지 않을 확률은 얼마인가?
+  * 이 확률 계산의 중요성에 (significance) 대해서 확인할 것
+Question
+  * 공항의 수하물가방 검색에서 무기가 발견될 확률은 5% 라고 한다.
+  * 검색결과가 정확할 확률은 90% 라고 한다.
+  * 검색에서 무기가 발견되었는데 사실은 무기가 아닐 확률은 (false positive) 얼마인가?